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Introduction to Linear Algebra
Rating: 4.2 out of 5(45 ratings)
1,980 students

Introduction to Linear Algebra

From Vectors to Matrices: A Comprehensive Introduction to Linear Algebra
Created byTensor Teach
Last updated 4/2023
English

What you'll learn

  • People looking to pursue a career in Data Science
  • High School or College Students
  • Aspiring Machine Learning Engineers
  • Lifelong learners

Course content

4 sections • 13 lectures • 1h 7m total length

  • Adding & Scaling Vectors5:30

    Learn how to add vectors component-wise, perform scalar multiplication, and interpret subtraction as adding a negative multiple, using examples like u = (2,1) and v = (-1,2).

  • Calculating Vector Lengths & Normalizing Vectors5:48
  • Dot Products & Matrix Multiplication6:40

    Compute the dot product of two vectors via transpose and component-wise multiplication, with a worked example. Then learn matrix multiplication, its output dimensions, and the inner-dimension requirement.

  • Determinant & Inverse of 2x2 Matrix2:43

    Compute the determinant of a two by two matrix by diagonal products minus; then find its inverse by multiplying one over the determinant with swapped diagonals and negated off-diagonals.

  • Vectors & Matrix Operations

Requirements

  • High School Algebra

Description

Introduction to Linear Algebra is a foundational course designed to provide students with a solid understanding of the fundamental concepts and techniques of linear algebra. Throughout the course, students will explore vectors and matrix operations, systems of linear equations, eigenvalues/vectors, diagonalization, linear transformations, bases, and subspaces, which are all key components of this important mathematical field.

Students will begin by studying the basic properties of vectors and matrices, including how to perform vector addition, scalar multiplication, and matrix operations. They will also learn how to solve systems of linear equations, both algebraically and graphically.

Moving on, students will delve into the concept of eigenvalues and eigenvectors, exploring how they relate to linear transformations and diagonalization. They will also investigate subspaces, bases, and span briefly in order to gain an awareness of the more abstract side of Linear Algebra.

Throughout the course, students will have the opportunity to develop their problem-solving skills through a variety of quiz questions. By the end of the course, students will have a strong foundation in linear algebra that will prepare them for further study in mathematics, engineering, computer science, and other fields that rely on this important subject. No matter whether you are an aspiring data scientist or you are already well into your career, this course can act as both a launching pad and a refresher on key concepts in linear algebra.

Who this course is for:

  • Beginner Data Scientists

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